Abhishek Srivastav

Maximally Bijective Discretization for data-driven modeling of complex systems

Phase-space discretization is a necessary step for study of continuous dynamical systems using a language-theoretic approach. It is also critical for many machine learning techniques, e.g., probabilistic graphical models (Bayesian Networks, Markov models). This paper proposes a novel discretization method - Maximally Bijective Discretization, that finds a discretization on the dependent variables given a discretization on the independent variables such that the correspondence between input and output variables in the continuous domain is preserved in discrete domain for the given dynamical system.

Information fusion for object & situation assessment in sensor networks

A semantic framework for information fusion in sensor networks for object and situation assessment is proposed. The overall vision is to construct machine representations that would enable human-like perceptual understanding of observed scenes via fusion of heterogeneous sensor data. In this regard, a hierarchical framework is proposed that is based on the Data Fusion Information Group (DFIG) model. Unlike a simple set-theoretic information fusion methodology that leads to loss of information, relational dependencies are modeled as cross-machines called relational Probabilistic Finite State Automata using the xD-Markov machine construction. This leads to a tractable approach for modeling composite patterns as structured sets for both object and scene representation. An illustrative example demonstrates the superior capability of the proposed methodology for pattern classification in urban scenarios.

Void fraction measurement in two-phase flow processes via symbolic dynamic filtering of ultrasonic signals

A slant-shelf magazine for an automatic, coin controlled, vending machine adapted to dispense cylindrical articles, such as canned or bottled beverages, which are stored and gravitationally fed from plural, parallel, horizontally inclined superposed storage racks into a vertical drop chute located opposite the lower ends of such racks. The drop chute communicates with a horizontally inclined delivery chute having a vend mechanism at its lowermost end for releasing articles one-by-one to a discharge hopper upon customer selection. The delivery chute is oppositely inclined from the storage racks and is joined to the drop chute by an intervening curvilinear guideway formed to reverse the gravitational movement direction of the articles prior to entry into the delivery chute for purposes of reducing article load forces on the vend mechanism.

Multi-sensor information fusion for fault detection in aircraft gas turbine engines

The article addresses data-driven fault detection in commercial aircraft gas turbine engines in the framework of multi-sensor information fusion and symbolic dynamic filtering. The hierarchical decision and control structure, adopted in this article, involves construction of composite patterns, namely, atomic patterns extracted from single sensors, and relational patterns representing cross-dependence between a pair of sensors. While the underlying theories are presented along with necessary assumptions, the proposed method is validated on the NASA C-MAPSS simulation test bed of aircraft gas turbine engines; both single-fault and multiple-fault scenarios have been investigated. Since aircraft engines undergo natural degradation during the course of their normal operation, the issue of distinguishing between a fault and natural degradation is also addressed.

A composite discretization scheme for symbolic identification of complex systems

Phase-space discretization is a necessary step for study of continuous dynamical systems using a symbolic dynamics and language-theoretic approach. It is also critical for many machine learning techniques, e.g., probabilistic graphical models (Bayesian Networks, Markov models). This paper proposes a novel composite discretization method - a univariate discretization, namely Statistical Similarity-based Discretization (SSD) followed by a multi-variate discretization called Maximally Bijective Discretization (MBD). While SSD first quantizes input variables for a complex system identifying different operating conditions, MBD finds a discretization on the output variables given the discretization on the input variables such that the correspondence between input and output variables in the continuous domain is preserved in discrete domain for the underlying dynamical system. The proposed method is applied on both simulated and experimental data and results are compared with classical uniform width, maximum entropy, clustering and self-organizing map based discretization techniques. HighlightsA composite discretization technique for input-output data of dynamical systems.Establish a relationship with admissible discretization for a dynamical system.Demonstration of efficacy on simulated and real systems.Comparison with state-of-the-art unsupervised discretization schemes.

Adaptive Sensor Activity Scheduling in Distributed Sensor Networks: A Statistical Mechanics Approach

This article presents an algorithm for adaptive sensor activity scheduling (A-SAS) in distributed sensor networks to enable detection and dynamic footprint tracking of spatial-temporal events. The sensor network is modeled as a Markov random field on a graph, where concepts of Statistical Mechanics are employed to stochastically activate the sensor nodes. Using an Ising-like formulation, the sleep and wake modes of a sensor node are modeled as spins with ferromagnetic neighborhood interactions; and clique potentials are defined to characterize the node behavior. Individual sensor nodes are designed to make local probabilistic decisions based on the most recently sensed parameters and the expected behavior of their neighbors. These local decisions evolve to globally meaningful ensemble behaviors of the sensor network to adaptively organize for event detection and tracking. The proposed algorithm naturally leads to a distributed implementation without the need for a centralized control. The A-SAS algorithm has been validated for resource-aware target tracking on a simulated sensor field of 600 nodes.

Depth estimation in Markov models of time-series data via spectral analysis

Symbol sequences are generated from observed time series data to construct probabilistic finite state automata (PFSA) models that capture the evolution of the dynamical system under consideration. One of the key challenges here is to estimate the relevant history or depth (i.e., the size of temporal memory) of the symbol sequences; in this context, spectral decomposition of the one-step transition matrix has been recently proposed for depth estimation. This paper compares the performance of depth estimation by spectral analysis with that of other commonly used metrics (e.g., log-likelihood, entropy rate and signal reconstruction) for analysis of symbolic dynamic systems. For experimental validation of the proposed concept, time-series data of fatigue damage evolution in a polycrystalline alloy, collected on a laboratory apparatus, have been discretized to generate symbol sequences. The depths, estimated by the spectral decomposition method, are then compared with those obtained by other metrics, and the results are found to be in close agreement. Furthermore, unsupervised clustering of time-series data, obtained for a number of test specimens in the fatigue-test experiments, demonstrates the efficacy of the proposed depth estimation method as well as the accuracy of depth estimation via spectral analysis and PFSA model construction.

Distributed decision propagation in mobile agent networks

This paper develops a distributed algorithm of decision/awareness propagation in mobile agent systems with a time varying network topology and threshold based agent interaction policy. While message broadcast duration or state updating interval is found to be an actuation parameter for changing time-averaged network topology, the threshold parameter in binary decision policy can be used to trigger or restrain the decision propagation. The influence of (large) seed size on the propagation phenomenon has been exploited to control the threat level threshold, beyond which the awareness propagates throughout the network.

Understanding phase transition in communication networks to enable robust and resilient control

This paper presents an application of Statistical Mechanics for analysis of critical phenomena in complex networks. Using the simulation model of a wired communication grid, the nature of phase transition is characterized and the corresponding critical exponent is computed. Network analogs of thermodynamic quantities such as order parameter, temperature, pressure, and composition are defined and the associated network phase diagrams are constructed. The notion of network eutectic point is introduced by showing characteristic similarities between the network phase diagram and the binary phase diagram. A concept of robust and resilient control in communication networks is presented based on network phase diagrams.

Estimating the size of temporal memory for symbolic analysis of time-series data

This paper presents an approach for symbolic analysis of time-series data from a dynamical system perspective that uses Markov modeling of symbol sequences. A key aspect of this approach is the selection of relevant histories or depth of the symbol sequence to capture the evolution of the observed dynamical system in its phase-space. An approach based on the spectral properties of the one-step transition matrix is proposed. A key advantage of this approach compared to the state-of-the-art is that it does not require several passes through the time-series data to search for the optimal model given some metric. The proposed approach makes use of the decay-rate of conditional influence of the current symbol to the n-step future of the dynamical system. Using a bound on this decay rate, the optimal depth can be computed in exactly one pass though the time-series data. The effectiveness of the proposed methodology is demonstrated on a known low-dimensional chaotic system and the efficacy of the approach for anomaly detection is demonstrated.